Phoroptors, also known as subjective refractors, are used in most eye examinations to measure refractive error (e.g. nearsightedness, astigmatism). Subjective refractors are used to refract, or bend, the light entering the eye, modifying its focus and thus the sharpness of the image formed on the retina. The clarity of focus is reported by the subject, hence the name subjective refractor. Systematic procedures are required for the accurate determination of nearsightedness (myopia) or farsightedness (hyperopia), and astigmatism. These procedures involve manipulation of the lens powers by the examiner, and repeated questioning of the subject, e.g. “which is better, lens 1 lens 2?”.
Conventional instruments employ spherical and cylindrical lenses, and a particular spherocylindrical power can be achieved by appropriate selection of sphere power, cylinder power, and cylinder axes. A significant problem with conventional instruments, however, is that complicated instruments and clinical procedures are required to reliably converge on the endpoint. Conventional refractors incorporate 10 or more separate cylindrical, or astigmatic, lenses. In addition, each of these lenses must be rotatable through at least 180°. These instruments and procedures are necessary due to the non-orthogonal nature of the conventional measures of dioptric power—sphere, cylinder, and axis. When either cylinder power or axis is changed, the spherocylindrical power does not change along just one dimension.
An analog of a conventional phoroptor is a slide projector with three focus knobs. Each of the three knobs must be set to the correct position for optimum focus. The non-orthogonality of sphere, cylinder, and axis means that as one knob is adjusted, the optimum position for one or both other knobs also changes. Consequently, clinical refraction with a conventional instrument requires systemic procedures to check and re-check sphere, cylinder and/or axis in order to reliably converge on the final endpoint.
Spherocylindrical dioptric powers are conventionally represented by a sphere power, a cylinder power, and a cylinder axis. These three parameters are not independent, and this may lead directly to a number of difficulties. The most often recognized instance of non-independence is the non-zero spherical equivalent power of a cylindrical lens.
An alternative representation of spherocylindrical power has significant advantages. This alternative representation has been rapidly gaining recognition in recent years, although it appeared in the literature some 30 years ago. As with other rapidly developing fields, new terminology has proliferated, which sometimes lacks consistency with that of others, and fails to identify overlap or relationships between terms of different sets. For simplicity, this application adopts the terminology first used by L. N. Thibos, W. Wheeler and D. Homer in “Power vectors: An application of fourier analysis to the description and statistical analysis of refractive error,” Optom Vis Sci 74(6): 367-75 (1997).
Wheeler and Homer described spherocylindrical dioptric power as consisting of a spherical equivalent (or mean power, M), and two components of astigmatism, J0 and J45. These two terms get their particular names because they can be represented by Jackson crossed cylinders with axes at 0°/90° and 45°/135°, respectively. These two astigmatic components define a plane of astigmatism, with the J0 and J45 axes corresponding to the x- and y-axes. The mean power line, M, is perpendicular to this plane of astigmatism, so together the three axes define a three-dimensional space, within which exists every spherocylindrical dioptric power.
FIG. 1 illustrates this three-dimensional dioptric space, defined by the three orthogonal axes, M, J0, and J45. The units along each of these three axes are diopters, and each point within this space is a unique spherocylindrical power.
The arithmetic relationships of sphere, cylinder, and axis, to M, J0, and J45 are straightforward. They are:M=Sph+Cyl/2  (1)                              J          0                =                              -                                          C                ⁢                                                                   ⁢                y                ⁢                                                                   ⁢                l                            2                                ×                      cos            ⁡                          (                              2                ×                A                ⁢                                                                   ⁢                x                ⁢                                                                   ⁢                i                ⁢                                                                   ⁢                s                            )                                                          (        2        )                                          J          45                =                              -                                          C                ⁢                                                                   ⁢                y                ⁢                                                                   ⁢                l                            2                                ×                      sin            ⁡                          (                              2                ×                A                ⁢                                                                   ⁢                x                ⁢                                                                   ⁢                i                ⁢                                                                   ⁢                s                            )                                                          (        3        )            
M is simply the usual spherical equivalent, or mean power of the system. After doubling the axis, J0 and J45 are the projections of half the cylinder power onto the x- and y-axes of the plane of astigmatism.
Converting from M, J0, and J45 to Sph, Cyl and Axis:                               S          ⁢                                           ⁢          p          ⁢                                           ⁢          h                =                  M          +                                                    J                0                2                            +                              J                45                2                                                                        (        4        )                                          C          ⁢                                           ⁢          y          ⁢                                           ⁢          l                =                              -            2                    ×                                                    J                0                2                            +                              J                45                2                                                                        (        5        )                                          A          ⁢                                           ⁢          x          ⁢                                           ⁢          i          ⁢                                           ⁢          s                =                                            tan                              -                1                                      ⁡                          (                                                J                  45                                                  J                  0                                            )                                2                                    (        6        )            
Attempts to improve upon conventional phoroptors have been described or produced in the past. One such instrument, described in “A Remote Subjective Refractor Employing Continuously Variable Sphere-Cylinder Corrections” by William E. Humphrey, Optical Engineering, 15, 286-291 (1976) and in U.S. Pat. No. 3,927,933 to William E. Humphrey, used special lenses described in “Development of variable focus lenses and a new refractor” by Luis E. Alvarez, Journal of the American Optometric Association, 49, 24-9 (1978) and in U.S. Pat. No. 3,507,565 to Luis E. Alvarez and William E. Humphrey to provide astigmatic decomposition.
Conventionally, astigmatism is expressed, and measured, in polar coordinates, i.e. having a magnitude (or amount), and an orientation (or direction). Astigmatic decomposition expresses astigmatism in Cartesian coordinates, i.e. having X- and Y-axis values. An instrument that implements astigmatic decomposition simplifies the measurement of astigmatism, with the same or better accuracy as compared to conventional instruments.
Measurement of astigmatism employing astigmatic decomposition simplifies the measurement because the two values (X and Y) of astigmatism are independent, unlike the conventional means of measuring it in polar coordinates. That is, because the X and Y astigmatism values are independent, they do not interact during measurement, in contrast to the conventional method, wherein changing one value affects the optimum value of the other.
In addition, a feature which distinguishes such an instrument from conventional instruments is that the two components of astigmatism are independent of the sphere (i.e. the correction for nearsightedness or farsightedness). This type of instrument may be referred to as a vector refractor, owing to the vector representation of spherocylindrical powers.
Humphrey's instrument was not a commercial success, despite its unique features. Contributing factors included the size of the machine, which usually required a dedicated room; expense—the machine performed similar functions to other instruments that cost 1/10th as much; lack of understanding of the theory and operation of the instrument; and the necessity for re-training of office staff and re-arrangement of office routine.
Other instruments have been described which implement astigmatic decomposition with two pairs of counter-rotating cylindrical lenses (i.e. “Stokes” lenses) (U.S. Pat. No. 3,822,932 to Humphrey et al and U.S. Pat. No. 4,943,162 to Sims) The Sims system had many of the same problems as the Humphrey instrument. It used astigmatic decomposition, but did so with five lenses per eye (more complexity/moving parts), and could only operate in “astigmatic decomposition” mode.
There have also been important developments in objective refractors and autorefraction. Autorefractors, however, have not eliminated the need for subjective refractors. At the very least, the results of subjective refraction serve as the final verification of a refractive procedure, regardless of how the preliminary refraction was performed. In addition, subjective refraction actively involves the patient in the process of arriving at a refractive correction. That fact alone does, to some degree, elevate the importance of subjective refraction, and confers upon it a level of legitimacy in the eyes of the examiner and the patient, which is not gained through objective refraction.